中国物理B ›› 2023, Vol. 32 ›› Issue (3): 30504-030504.doi: 10.1088/1674-1056/ac7dbb

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Asymmetric image encryption algorithm based on a new three-dimensional improved logistic chaotic map

Guo-Dong Ye(叶国栋)1,2,†, Hui-Shan Wu(吴惠山)1, Xiao-Ling Huang(黄小玲)1, and Syh-Yuan Tan3   

  1. 1 Faculty of Mathematics and Computer Science, Guangdong Ocean University, Zhanjiang 524088, China;
    2 Guangdong Provincial Engineering and Technology Research Center of Far Sea Fisheries Management and Fishing of South China Sea, Zhanjiang 524088, China;
    3 School of Computing, Newcastle University, Newcastle NE4 5TG, UK
  • 收稿日期:2022-03-29 修回日期:2022-05-24 接受日期:2022-07-02 出版日期:2023-02-14 发布日期:2023-03-03
  • 通讯作者: Guo-Dong Ye E-mail:guodongye@hotmail.com
  • 基金资助:
    This work was supported in part by the National Natural Science Foundation of China (Grant No. 61972103), the Natural Science Foundation of Guangdong Province of China (Grant No. 2023A1515011207), the Special Project in Key Area of General University in Guangdong Province of China (Grant No. 2020ZDZX3064), the Characteristic Innovation Project of General University in Guangdong Province of China (Grant No. 2022KTSCX051), the Postgraduate Education Innovation Project of Guangdong Ocean University of China (Grant No. 202263), and the Foundation of Guangdong Provincial Engineering and Technology Research Center of Far Sea Fisheries Management and Fishing of South China Sea.

Asymmetric image encryption algorithm based on a new three-dimensional improved logistic chaotic map

Guo-Dong Ye(叶国栋)1,2,†, Hui-Shan Wu(吴惠山)1, Xiao-Ling Huang(黄小玲)1, and Syh-Yuan Tan3   

  1. 1 Faculty of Mathematics and Computer Science, Guangdong Ocean University, Zhanjiang 524088, China;
    2 Guangdong Provincial Engineering and Technology Research Center of Far Sea Fisheries Management and Fishing of South China Sea, Zhanjiang 524088, China;
    3 School of Computing, Newcastle University, Newcastle NE4 5TG, UK
  • Received:2022-03-29 Revised:2022-05-24 Accepted:2022-07-02 Online:2023-02-14 Published:2023-03-03
  • Contact: Guo-Dong Ye E-mail:guodongye@hotmail.com
  • Supported by:
    This work was supported in part by the National Natural Science Foundation of China (Grant No. 61972103), the Natural Science Foundation of Guangdong Province of China (Grant No. 2023A1515011207), the Special Project in Key Area of General University in Guangdong Province of China (Grant No. 2020ZDZX3064), the Characteristic Innovation Project of General University in Guangdong Province of China (Grant No. 2022KTSCX051), the Postgraduate Education Innovation Project of Guangdong Ocean University of China (Grant No. 202263), and the Foundation of Guangdong Provincial Engineering and Technology Research Center of Far Sea Fisheries Management and Fishing of South China Sea.

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摘要： Based on some analyses of existing chaotic image encryption frameworks and a new designed three-dimensional improved logistic chaotic map (3D-ILM), an asymmetric image encryption algorithm using public-key Rivest-Shamir-Adleman (RSA) is presented in this paper. In the first stage, a new 3D-ILM is proposed to enhance the chaotic behavior considering analysis of time sequence, Lyapunov exponent, and Shannon entropy. In the second stage, combined with the public key RSA algorithm, a new key acquisition mathematical model (MKA) is constructed to obtain the initial keys for the 3D-ILM. Consequently, the key stream can be produced depending on the plain image for a higher security. Moreover, a novel process model (NPM) for the input of the 3D-ILM is built, which is built to improve the distribution uniformity of the chaotic sequence. In the third stage, to encrypt the plain image, a pre-process by exclusive OR (XOR) operation with a random matrix is applied. Then, the pre-processed image is performed by a permutation for rows, a downward modulo function for adjacent pixels, a permutation for columns, a forward direction XOR addition-modulo diffusion, and a backward direction XOR addition-modulo diffusion to achieve the final cipher image. Moreover, experiments show that the the proposed algorithm has a better performance. Especially, the number of pixels change rate (NPCR) is close to ideal case 99.6094%, with the unified average changing intensity (UACI) close to 33.4634%, and the information entropy (IE) close to 8.

关键词: three-dimensional improved logistic chaotic map (3D-ILM), Rivest-Shamir-Adleman (RSA) algorithm, image encryption, confusion, entropy

Abstract: Based on some analyses of existing chaotic image encryption frameworks and a new designed three-dimensional improved logistic chaotic map (3D-ILM), an asymmetric image encryption algorithm using public-key Rivest-Shamir-Adleman (RSA) is presented in this paper. In the first stage, a new 3D-ILM is proposed to enhance the chaotic behavior considering analysis of time sequence, Lyapunov exponent, and Shannon entropy. In the second stage, combined with the public key RSA algorithm, a new key acquisition mathematical model (MKA) is constructed to obtain the initial keys for the 3D-ILM. Consequently, the key stream can be produced depending on the plain image for a higher security. Moreover, a novel process model (NPM) for the input of the 3D-ILM is built, which is built to improve the distribution uniformity of the chaotic sequence. In the third stage, to encrypt the plain image, a pre-process by exclusive OR (XOR) operation with a random matrix is applied. Then, the pre-processed image is performed by a permutation for rows, a downward modulo function for adjacent pixels, a permutation for columns, a forward direction XOR addition-modulo diffusion, and a backward direction XOR addition-modulo diffusion to achieve the final cipher image. Moreover, experiments show that the the proposed algorithm has a better performance. Especially, the number of pixels change rate (NPCR) is close to ideal case 99.6094%, with the unified average changing intensity (UACI) close to 33.4634%, and the information entropy (IE) close to 8.

Key words: three-dimensional improved logistic chaotic map (3D-ILM), Rivest-Shamir-Adleman (RSA) algorithm, image encryption, confusion, entropy

中图分类号:  (Control of chaos, applications of chaos)

  • 05.45.Gg
05.45.Ac (Low-dimensional chaos) 07.05.Pj (Image processing)